Instead of trying to write the outbound CID early in the call flow as you are currently, set a unique channel variable to track the call, i.e.:
exten => s,n,Set(__queue_cid="Tech Support" <{redacted}6102>) ; leading double underscore may or may not be necessary
exten => s,n,Goto(ext-queues,610201,1)
The channel var will carry the desired CID, which you can then set at the very last point prior to leaving the system by:
[macro-dialout-trunk-predial-hook]
exten => s,1,ExecIf($["${queue_cid}"!=""]?Set(CALLERID(all)=${queue_cid})
mw;dt (might work; didn’t test)